MathDB

A 24

Source:

May 25, 2007

floor functionmodular arithmeticDivisibility Theory

Problem Statement

Let

p>3

is a prime number and

k=\lfloor\frac{2p}{3}\rfloor

. Prove that

{p \choose 1}+{p \choose 2}+\cdots+{p \choose k}

is divisible by

p^{2}